We give an example of a coherent theory, a topological space, and a continuous assignment of the (model-theoretic) types of the theory to the points of the space, such that there is no sheaf model of the theory over the space with the property that the fibre over a point, as a set-based model, realises the corresponding type; thus, we answer in the negative a problem posed by Krist\'of Kanalas.
We construct a simple expansion of the theory of nonabelian free groups in which the group admits a global type with bounded left-translation orbit but is not definably amenable. This extends the construction of Chernikov, Hrushovski, Kruckman, Krupi\'nski, Moconja, Pillay, and Ramsey, and gives a counterexample to Pet...
Settling a central problem in set-theoretic topology, and many related problems, we prove that there is, consistently, a regular Lindel\"of space of cardinality $\aleph_1$ that is not a D-space. The existence of such a space is independent of ZFC; we establish its equivalence to a weak form of the Continuum Hypothesis....
In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield
K
of the real numbers that lacks several such tameness properties. As our main result, we present a first-order formula in the language of rings defining a se...
Lothar Sebastian Krapp, Matthieu Vermeil, Laura Wirth· Publications mathématiques...· 2 citations
We give an $\infty$-categorical enhancement of Neisendorfer's equivalences between the homotopy categories of rational simplicial sets, commutative dg algebras (cdgas), cocommutative dg coalgebras (cdgcs) and dg Lie algebras (dgls), where these objects have respective hypotheses of connectedness, nilpotency and finite...
We generalize Serre's conditions for coherent sheaves to triangulated categories equipped with a $t$-structure and duality, which we call Verdier-type categories. We present examples of such categories and their associated Serre conditions, then focus on constructible sheaves, where we refer to these conditions as geom...
We build on the recent development that toposes with enough points can be represented as categories of points equipped with ultraconvergence data (a.k.a. virtual ultracategories), characterizing usual classes of geometric morphisms --- surjections, embeddings, hyperconnected maps, and localic maps --- in terms of their...
Saadia Gabriel, Yuksel Errol· 0 citations
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